Do you know the differences between the bourke and grass parakeet? Temperament-wise it's hard to distinguish the main differencesCalmness, in general: Bourke parakeets and diamond doves.
Had both and they were very calm.
It will of course depend on where you get them from. My diamond dove came from a pet store and it took him a while to warm up to me and I also worked with him (but not much) to teach him step up.